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putting ice into water: the ice and water are in contact with each other over a large surface area this allows more efficient heat transfer.

putting a bucket of water into ice: Energy in the form of heat must pass through the bucket to the ice which is more difficult.

Also the is less contact area with the solid ice sitting against the bucket than if water was in contact with the bucket. This is why when u make an ice bath to cool something down in you add water, it increases the contact area.

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